Elliptic curve isogeny class 1600.2-g over number field \(\Q(\sqrt{21}) \)

• Base field: \(\Q(\sqrt{21}) \)
• Label: 2.2.21.1-1600.2-g
• Conductor: 1600.2
• Rank: \( 0 \)

Base field \(\Q(\sqrt{21}) \)

Generator \(a\), with minimal polynomial \( x^{2} - x - 5 \); class number \(1\).

Elliptic curves in class 1600.2-g over \(\Q(\sqrt{21}) \)

Isogeny class 1600.2-g contains 2 curves linked by isogenies of degree 2.

Curve label	Weierstrass Coefficients
1600.2-g1	\( \bigl[0\) , \( -a\) , \( 0\) , \( -22 a - 35\) , \( 103 a + 190\bigr] \)
1600.2-g2	\( \bigl[0\) , \( -a\) , \( 0\) , \( -342 a - 635\) , \( 5655 a + 10150\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rr} 1 & 2 \\ 2 & 1 \end{array}\right)\)

Isogeny graph